Linux touchscreen support is in the kernel, so that's not an issue. I have a touchscreen machine (Lenovo Think Centre Graphics Tablet) and the touch interface works quite nicely under Linux, though I seldom use touch--it's easier to use keyboard/mouse for how I use that particular machine.
As for a "skinnable" Desktop Environment/Window Manager, that may be a whole different issue. Some DE/WMs are more configurable than others, but I've not run into one that is "skinnable," in the sense of user being able to overlay an entire interface over the existing GUI environment, as opposed to configuring the existing elements to your liking. In my experience, skinnability is more a application level thing, as for browsers, media players, and the like.
Off the top of my head, I think that KDE might be your best choice. You could use the
KDE "Activities" to design an "Activity" meets your needs, but that would certainly not be the same thing as "skinning" KDE.